In the last few years it has been shown that a wide variety of triaxial magnetic fields can produce strong fluid vorticity. See J. E. Martin, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 79, 011503 (2009); J. E. Martin and K. J. Solis, Soft Matter 10, 3993 (2014); K. J. Solis and J. E. Martin, Soft Matter 10, 6139 (2014); J. E. Martin and K. J. Solis, Soft Matter 11, 241 (2015); and U.S. application Ser. No. 12/893,104, each of which is incorporated herein by reference. These fields are comprised of three mutually orthogonal field components, of which either two or three are alternating, and whose various frequency ratios are rational numbers. These dynamic fields generally lack circulation, in that a magnetically soft ferromagnetic rod subjected to one of these fields does not undergo a net rotation during a field cycle. Yet these fields do induce deterministic vorticity, which might seem counterintuitive. For this deterministic vorticity to occur it must be reversible. This reversibility is possible if the trajectory of the field and its physically equivalent converse, considered jointly, is reversible. This field parity occurs because the symmetry of this union of fields is shared by vorticity, which is reversible.
An analysis of the symmetry of these fields enables the prediction of the vorticity axis, which is determined solely by the relative frequencies of the triaxial field components. For these fields changing the relative phases of the components enables control of the magnitude and sign of the vorticity—and in some cases changing the sign of the dc field also reverses flow—but not the axis around which vorticity occurs. Thus, when the frequency of one of the field components is detuned slightly to cause a slow phase modulation, the vorticity will periodically reverse, but it remains fixed around a single axis. Such flows produce a simple form of periodic stirring, as occurs in a washing machine.
The present invention goes well beyond this simple form of stirring and is based on transitions in the symmetry of the triaxial field.